What hurts his chances in this regard is that the opinion of an NFL scout was that GT was not a scout friendly visit. Johnson didn't provide anything that refuted that. Had he pointed to other scouts that would have had different opinions then sure. But he didn't. His comment about not remembering the guy only plays into the idea of limited access to coaches being an issue and his denials wouldn't really convince employers not to look into it. That being said in this regard I highly doubt this matters. Future employers would probably more concerned with Johnson being able to satisfy them that he can field a competent defense to go with his offense, and probably a dozen other issues, before being a scout friendly visit.
To me, the main reason I think he should have let it go is that the account he is on is still officially affiliated with GT. His use of it should still be entirely to the benefit of GT, and I don't believe his response was that because at the core, Nagy's tweet was a positive one for GT building hype for the new staff from an outside source which we need. Now he is free to respond of course, but he should have done it from a personal twitter, not the one described as "Official Twitter for
@GeorgiaTechFB" . I also believe that if he is a fan of GT, as he said he always would be, he could overlook a very minor slight in a post that was overall positive for the program.